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Research Areas

Wide range of faculty research

List of Faculty Research Areas

N. Higson K-theory, Representation Theory
J. Huizenga Algebraic Geometry
S. Katok  Fuchsian Groups
J. Lesieutre Algebraic Geometry
J. Morton Algebraic Geometry, Computational Complexity
A. Ocneanu Classical and Quantum Groups
M. Stienon Algebra, Homological Algebra
L. Vaserstein Classical Groups over Rings, Algebraic K-Theory
P. Xu Homotopy Algebras,  Higher Structures
Y. Zarhin Algebraic Geometry

I. Aronson Active materials, cell motility
A. Belmonte Fragmentation, Dynamic Buckling
L. Berlyand Homogenization Theory, Composites
W. Cao Material Science
X. Li Multiscale Modeling in Crystals
A. Mazzucato Elasticity, Inverse Problems
A. Novikov Composites, Martensitic Transitions in Polycrystals

J. Bochi  Dynamical Systems, Geometry 
N. Brown Noncommutative Dynamical Systems
D. Burago Dynamical Systems
B. Kalinin Dynamical Systems and Ergodic Theory
S. Katok Dynamical Systems and Applications to Analysis and Number Theory
J. Lesieutre Algebraic and Arithmetic Dynamics
M. Levi Dynamical Systems and Applications to Physics and Engineering
Y. Pesin Dynamical Systems, Ergodic Theory, Dimension Theory, Statistical Physics
F. Rodriguez-Hertz Dynamical Systems, Ergodic Theory
V. Sadovskaya Dynamical Systems and Ergodic Theory
S. Schmieding  Dynamical Systems and Ergodic Theory
S. Tabachnikov Dynamical Systems
L. Westrick Symbolic Dynamics

I. Aronson Flow of living liquid crystals
A. Belmonte Viscoelastic Fluids, Free Surfaces, Reactive Flows
D. Henderson Nonlinear Waves
K. Jenssen Compressible Flows
M. Levi Ideal Fluids
A. Mazzucato Navier-Stokes and Euler equations, turbulence, mixing
T. Nguyen Navier-Stokes equations, Boundary layer theory
A. Novikov Turbulence
W. Shen granular flow, traffic flow, polymer flooding in two phase flow, reservoir simulation
J. Xu Simulation of Non-Newtonian Fluids

N. Brown Operator Algebras
P. Baum Operator Algebras, K-Theory
N. Higson Operator Algebras, K-theory, Noncommutative Geometry
A. Ocneanu Operator Algebras

P. Baum Algebraic Topology
D. Burago Riemannian Geometry
A. Banyaga Symplectic Topology, Contact Geometry
J. Case Conformal and CR Geometry
C. Curto Applied Algebra, Topology and Geometry
N. Higson Operator Algebras, K-theory, Noncommutative Geometry
J. Huizenga Algebraic Geometry
V. Itskov Applied Algebraic Topology and Geometry
B. Kalinin Geometry
S. Katok Hyperbolic Geometry and Fuchsian Groups
J. Lesieutre Algebraic Geometry
M. Levi Differential Geometry and Classical Mechanics
L.-C. Li Poisson Geometry
J. Morton Algebraic Geometry, Tropical Geometry
Y. Pesin Riemannian Geometry
A. Petrunin Singular Geometry, Topology, Combinatorial Geometry
F. Rodriguez-Hertz Geometry
M. Stienon Poisson geometry, dg manifolds, groupoids and stacks
S. Tabachnikov Symplectic Geometry, Differential Geometry and Topology, Knots
A. Wade Differential Geometry
P. Xu Symplectic Geometry, Noncommutative Geometry
Y. Zarhin Algebraic Geometry

I. Aronson Collective dynamics of motile cells and bacteria
A. Belmonte Cooperative cell motion, biological fluid dynamics, evolutionary games
L. Berlyand Active Biological Systems: Biosuspensions and cell motility
A. Bressan Free Boundary Problems Modeling Tissue Growth
J. Conway Infectious Disease Modeling
C. Curto Theoretical and Computational Neuroscience, Neural Network Theory and Neural Coding
W. Hao Computational modeling in biomedical diseases
V. Itskov Theoretical Neuroscience, Neural networks and Learning
T. RelugaPopulation Biology, Ecology and Infectious Disease Modeling
W. Shen PDE models for stems and leaves
H. Weiss The population and evolutionary dynamics of populations of bacteria and the pharmacodynamics of antibiotics and bacteriophage, especially in physical structure; transmission of respiratory infections; microbiome assembly, dynamics and stability

K. Eisentraeger Hilbert's Tenth Problem
J. Reimann Logic, Computability, Algorithmic Information Theory and Randomness
L. Westrick Computability, Descriptive Set Theory

L.-C. Li Integrable Systems
A. Ocneanu Topological and Quantum Field Theory
M. Stienon Quantization
A. Wade Poisson Geometry
P. Xu Quantization, Supergeometry

S. Akhtari  Number Theory, Diophantine Analysis, Geometry of Numbers
G. Andrews Partitions, Number Theory, Applications
D. Brownawell Number Theory
K. Eisentraeger Cryptography, Number Theory, Arithmetic Geometry
S. Katok Automorphic Forms
W. Li Number Theory, Representation Theory, Coding Theory, Spectral Graph Theory
G. Mullen Finite Fields, Combinatorics
M. Papikian Algebraic Number Theory, Arithmetic Geometry
N. Talebizadeh Sardari Theory, Sphere Packing, Expander Graphs and Quantum Chaos
L. Vaserstein Number Theory
R. Vaughan Analytic Number Theory
A. Yee Partition Theory, Enumerative Combinatorics

I. Aronson Numerical methods for partial differential equations, GPU computations
J. Brannick Computational Fluid Dynamics and Chromodynamics
W. HaoComputational math, homotopy continuation methods
J. Harlim Numerical Analysis
X. Li Computational Mechanics
W. Shen Numerical Simulation
J. Xu Computational Analysis, Numerical Methods, Multigrid, Deep Learning
L. Zikatanov Computational Mathematics, Numerical Analysis

L. Berlyand Partial Differential Equations, Calculus of Variations
A. Bressan Hyperbolic Conservation Laws, Nonlinear Wave Equations, Models of Traffic Flow on Networks
P-E Jabin Multi-Agent Systems, Transport and Advection Equations
K. Jenssen Conservation Laws, Compressible Flow
L.-C. Li Integrable Systems
A. Mazzucato equations of continuum mechanics (fluid flow and elasticity), inverse problems, harmonic and microlocal analysis
T. Nguyen Navier-Stokes equations, Kinetic theory of gases, Dynamics of nonlinear waves, Boundary layers
A. Novikov Partial Differential Equations, Analysis
W. Shen Hyperbolic Conservation Laws, Relaxation, Partial Differential Equations
Y. Zheng Partial Differential Equations

J. Conway Probability and Biology
M. Denker Probability and its applications
L.-C. Li Random Matrices
X. Li Modeling and Computations with Stochastic Differential Equations
J. Morton Covariance Matrices, Cumulant Tensors
A. Novikov Stochastic Differential Equations
Y. Pesin Probability and Statistics
T. Reluga Probability and Biology

A. Belmonte  Game Theory Dynamics
L. Berlyand Social networks
A. Bressan Optimal control, Differential Games and Applications to Economics and Finance
N. Brown Diversity in STEM
C. Byrne Integration of Game Theory & Psychology, Agent-Based Emergent Dynamics, Mathematical Modeling & Optimization
J. Li  Mathematical Economics, Finance, Monetary Economics
A. Mazzucato  mathematical finance, option pricing
T. Reluga  Game Theory of Disease Management
W. Shen  differential games and applications, optimal control
L. Vaserstein  Operational Research, Game Theory